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- W2078447047 abstract "We consider N Brownian particles moving on a line starting from initial positions $$mathbf{{u}}equiv {u_1,u_2,ldots u_N}$$ such that $$0<u_1 < u_2 < cdots < u_N$$ . Their motion gets stopped at time $$t_s$$ when either two of them collide or when the particle closest to the origin hits the origin for the first time. For $$N=2$$ , we study the probability distribution function $$p_1(m|mathbf{{u}})$$ and $$p_2(m|mathbf{{u}})$$ of the maximal distance travelled by the $$1^{text {st}}$$ and $$2^{text {nd}}$$ walker till $$t_s$$ . For general N particles with identical diffusion constants $$D$$ , we show that the probability distribution $$p_N(m|mathbf{u})$$ of the global maximum $$m_N$$ , has a power law tail $$p_i(m|mathbf{{u}}) sim {N^2B_Nmathcal {F}_{N}(mathbf{u})}/{m^{nu _N}}$$ with exponent $$nu _N =N^2+1$$ . We obtain explicit expressions of the function $$mathcal {F}_{N}(mathbf{u})$$ and of the N dependent amplitude $$B_N$$ which we also analyze for large N using techniques from random matrix theory. We verify our analytical results through direct numerical simulations." @default.
- W2078447047 created "2016-06-24" @default.
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- W2078447047 date "2014-07-22" @default.
- W2078447047 modified "2023-10-16" @default.
- W2078447047 title "Maximal Distance Travelled by N Vicious Walkers Till Their Survival" @default.
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- W2078447047 doi "https://doi.org/10.1007/s10955-014-1064-1" @default.
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